Recent research has focused on modeling asset prices byItô semimartingales. In such a modeling framework,the quadratic variation consists of a continuous anda jump component. This paper is about inference onthe jump part of the quadratic variation, which canbe estimated by the difference of realized varianceand realized multipower variation. The maincontribution of this paper is twofold. First, itprovides a bivariate asymptotic limit theory forrealized variance and realized multipower variationin the presence of jumps. Second, this paperpresents new, consistent estimators for the jumppart of the asymptotic variance of the estimationbias. Eventually, this leads to a feasibleasymptotic theory that is applicable in practice.Finally, Monte Carlo studies reveal a good finitesample performance of the proposed feasible limittheory.

This paper investigates the asymptotic size propertiesof a two-stage test in the linear instrumentalvariables model when in the first stage a Hausman(1978) specification test is used as a pretest ofexogeneity of a regressor. In the second stage, asimple hypothesis about a component of thestructural parameter vector is tested, using at-statistic that is based oneither the ordinary least squares (OLS) or thetwo-stage least squares estimator (2SLS), dependingon the outcome of the Hausman pretest. Theasymptotic size of the two-stage test is derived ina model where weak instruments are ruled out byimposing a positive lower bound on the strength ofthe instruments. The asymptotic size equals 1 forempirically relevant choices of the parameter space.The size distortion is caused by a discontinuity ofthe asymptotic distribution of the test statistic inthe correlation parameter between the structural andreduced form error terms. The Hausman pretest doesnot have sufficient power against correlations thatare local to zero while the OLS-basedt-statistic takes on large valuesfor such nonzero correlations. Instead of using thetwo-stage procedure, the recommendation then is touse a t-statistic based on the 2SLSestimator or, if weak instruments are a concern, theconditional likelihood ratio test by Moreira(2003).

We derive the semiparametric efficiency bound indynamic models of conditional quantiles under a solestrong mixing assumption. We also provide anexpression of Stein’s (1956) least favorableparametric submodel. Our approach is as follows:First, we construct a fully parametric submodel ofthe semiparametric model defined by the conditionalquantile restriction that contains the datagenerating process. We then compare the asymptoticcovariance matrix of the MLE obtained in thissubmodel with those of the M-estimators for theconditional quantile parameter that are consistentand asymptotically normal. Finally, we show that theminimum asymptotic covariance matrix of this classof M-estimators equals the asymptotic covariancematrix of the parametric submodel MLE. Thus, (i)this parametric submodel is a least favorable one,and (ii) the expression of the semiparametricefficiency bound for the conditional quantileparameter follows.

The paper discusses contemporaneous aggregation of theLinear ARCH (LARCH) model as defined in (1), whichwas introduced in Robinson (1991) and studied inGiraitis, Robinson, and Surgailis (2000) and otherworks. We show that the limiting aggregate of the(G)eneralized LARCH(1,1) process in (3)–(4) withrandom Beta distributed coefficientβ exhibits long memory. Inparticular, we prove that squares of the limitingaggregated process have slowly decaying correlationsand their partial sums converge to a self-similarprocess of a new type.

This paper considers inference based on a teststatistic that has a limit distribution that isdiscontinuous in a parameter. The paper shows thatsubsampling and m out ofn bootstrap tests based on such atest statistic often have asymptotic size—defined asthe limit of exact size—that is greater than thenominal level of the tests. This is due to a lack ofuniformity in the pointwise asymptotics. Wedetermine precisely the asymptotic size of suchtests under a general set of high-level conditionsthat are relatively easy to verify. The results showthat the asymptotic size of subsampling andm out of nbootstrap tests is distorted in some examples butnot in others.

This paper considers parametric estimation problemswith independent, identically nonregularlydistributed data. It focuses on rate efficiency, inthe sense of maximal possible convergence rates ofstochastically bounded estimators, as an optimalitycriterion, largely unexplored in parametricestimation. Under mild conditions, the Hellingermetric, defined on the space of parametricprobability measures, is shown to be an essentiallyuniversally applicable tool to determine maximalpossible convergence rates. These rates are shown tobe attainable in general classes of parametricestimation problems.

Recently, Shimotsu and Phillips (2005, Annalsof Statistics 33, 1890–1933) developed anew semiparametric estimator, the exact localWhittle (ELW) estimator, of the memory parameter(d) in fractionally integratedprocesses. The ELW estimator has been shown to beconsistent, and it has the same asymptoticdistribution for all values of d,if the optimization covers an interval of width lessthan 9/2 and the mean of the process is known. Withthe intent to provide a semiparametric estimatorsuitable for economic data, we extend the ELWestimator so that it accommodates an unknown meanand a polynomial time trend. We show that thetwo-step ELW estimator, which is based on a modifiedELW objective function using a tapered local Whittleestimator in the first stage, has an asymptoticdistribution for (or when the datahave a polynomial trend). Our simulation studyillustrates that the two-step ELW estimator inheritsthe desirable properties of the ELW estimator.

The local linear method is popular in estimatingnonparametric continuous-time diffusion models, butit may produce negative results for the diffusion(or volatility) functions and thus lead toinsensible inference. We demonstrate this using U.S.interest rate data. We propose a new functionalestimation method of the diffusion coefficient basedon reweighting the conventional Nadaraya–Watsonestimator. It preserves the appealing biasproperties of the local linear estimator and isguaranteed to be nonnegative in finite samples. Alimit theory is developed under mild requirements(recurrence) of the data generating mechanismwithout assuming stationarity or ergodicity.

This paper establishes asymptotic properties ofquasi-maximum likelihood estimators for spatialdynamic panel data with both time and individualfixed effects when the number of individualsn and the number of time periodsT can be large. We propose a datatransformation approach to eliminate the timeeffects. When n / T → 0, theestimators are consistent andasymptotically centered normal; whenn is asymptotically proportionalto T, they are consistent andasymptotically normal, but the limit distribution isnot centered around 0; when n / T →∞, the estimators are consistent with rateT and have a degenerate limitdistribution. We also propose a bias correction forour estimators. When n1/3 /T → 0, the correction willasymptotically eliminate the bias and yield acentered confidence interval. The estimates from thetransformation approach can be consistent whenn is a fixed finite number.

This paper studies a procedure to combine individualforecasts that achieve theoretical optimalperformance. The results apply to a wide variety ofloss functions and only require a tail condition onthe data sequences. The theoretical results showthat the bounds are also valid in the case of timevarying combination weights.

In this paper we derive an alternative asymptoticapproximation to the sampling distribution of thelimited information maximum likelihood estimator anda bias-corrected version of the two-stage leastsquares estimator. The approximation is obtained byallowing the number of instruments and theconcentration parameter to grow at the same rate asthe sample size. More specifically, we allow forpotentially nonnormal error distributions and obtainthe conventional asymptotic distribution and theresults of Bekker (1994,Econometrica 62, 657–681) andBekker and Van der Ploeg (2005, StatisticaNeerlandica 59, 139–267) as specialcases. The results show that when the errordistribution is not normal, in general both theproperties of the instruments and the third andfourth moments of the errors affect the asymptoticvariance. We compare our findings with those in therecent literature on many and weak instruments.